Question: $-5ef + 7eg + 5e - 6 = f + 6$ Solve for $e$.
Solution: Combine constant terms on the right. $-5ef + 7eg + 5e - {6} = f + {6}$ $-5ef + 7eg + 5e = f + {12}$ Notice that all the terms on the left-hand side of the equation have $e$ in them. $-5{e}f + 7{e}g + 5{e} = f + 12$ Factor out the $e$ ${e} \cdot \left( -5f + 7g + 5 \right) = f + 12$ Isolate the $e$ $e \cdot \left( -{5f + 7g + 5} \right) = f + 12$ $e = \dfrac{ f + 12 }{ -{5f + 7g + 5} }$